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• • Contributed by OpenStax
• General Physics at OpenStax CNX

8.1. $$\displaystyle 1.1×10^{−3}m$$

8.3. 3.59 cm, 17.98 cm

8.4. a. 25.0 pF;

b. 9.2

8.5. a. $$\displaystyle C=0.86pF,Q_1=10pC,Q_2=3.4pC,Q_3=6.8pC$$;

b. $$\displaystyle C=2.3pF,Q_1=12pC,Q_2=Q_3=16pC$$;

c. $$\displaystyle C=2.3pF,Q_1=9.0pC,Q_2=18pC,Q_3=12pC,Q_4=15pC$$

8.6. a.$$\displaystyle 4.0×10^{−13}J$$; b. 9 times

8.7. a. 3.0; b. $$\displaystyle C=3.0C_0$$

8.9. a. $$\displaystyle C_0=20pF, C=42pF$$;

b. $$\displaystyle Q_0=0.8nC, Q=1.7nC$$;

c. $$\displaystyle V_0=V=40V$$; d. $$\displaystyle U_0=16nJ, U=34nJ$$

## Conceptual Questions

1. no; yes

3. false

5. no

7. $$\displaystyle 3.0μF,0.33μF$$

11. Dielectric strength is a critical value of an electrical field above which an insulator starts to conduct; a dielectric constant is the ratio of the electrical field in vacuum to the net electrical field in a material.

13. Water is a good solvent.

15. When energy of thermal motion is large (high temperature), an electrical field must be large too in order to keep electric dipoles aligned with it.

## Problems

19. 21.6 mC

21. 1.55 V

23. 25.0 nF

25. $$\displaystyle 1.1×10^{−3}m^2$$

27. 500 µC

29. 1:16

31. a. 1.07 nC;

b. 267 V, 133 V

33. $$\displaystyle 0.29μF$$

34. 500 capacitors; connected in parallel

35. $$\displaystyle 3.08μF$$ (series) and $$\displaystyle 13.0μ$$ (parallel)

37. $$\displaystyle 11.4μF$$

39. 0.89 mC; 1.78 mC; 444 V

41. $$\displaystyle 7.5μJ$$

43. a. 405 J; b. 90.0 mC

45. 1.15 J

47. a. $$\displaystyle 4.43×10^{−9}F$$;

b. 0.453 V;

c. $$\displaystyle 4.53×10^{−10}J$$;

d. no

49. 0.7 mJ

51. a. 7.1 pF;

b. 42 pF

53. a. before 3.00 V; after 0.600 V;

b. before 1500 V/m; after 300 V/m

55. a. 3.91;

b. 22.8 V

57. a. 37 nC;

b. 0.4 MV/m;

c. 19 nC

59. a. $$\displaystyle 4.4μF$$;

b. $$\displaystyle 4.0×10^{-5}C$$

61. $$\displaystyle 0.0135m^2$$

63. $$\displaystyle 0.185μJ$$

65. a. 0.277 nF;

b. 27.7 nC;

c. 50 kV/m

67. a. 0.065 F;

b. 23,000 C;

c. 4.0 GJ

69. a. $$\displaystyle 75.6μC$$; b. 10.8 V

71. a. 0.13 J;

b. no, because of resistive heating in connecting wires that is always present, but the circuit schematic does not indicate resistors 73. a. $$\displaystyle −3.00μF$$;

b. You cannot have a negative $$\displaystyle C_2$$ capacitance.

c. The assumption that they were hooked up in parallel, rather than in series, is incorrect. A parallel connection always produces a greater capacitance, while here a smaller capacitance was assumed. This could only happen if the capacitors are connected in series.

75. a. 14.2 kV;

b. The voltage is unreasonably large, more than 100 times the breakdown voltage of nylon.

c. The assumed charge is unreasonably large and cannot be stored in a capacitor of these dimensions.

## Challenge Problems

77. a. 89.6 pF;

b. 6.09 kV/m;

c. 4.47 kV/m;

d. no

79. a. 421 J;

b. 53.9 mF

81. $$\displaystyle C=ε_0A/(d_1+d_2)$$

83. proof